C Program To Calculate Values Using Fixed Point Iteration and Honors Method | C Programming

C Program To Calculate Values Using Fixed Point Iteration Method

Algorithm

1. Start
2. Read values of x0 and e.
   *Here x0 is the initial approximation
   e is the absolute error or the desired degree of accuracy, also the stopping criteria*
3. Calculate x1 = g(x0)
4. If [x1 – x0] <= e, goto step 6.
   *Here [ ] refers to the modulus sign*
5. Else, assign x0 = x1 and goto step 3.
6. Display x1 as the root.
7. Stop

#include<stdio.h>
#include<math.h>
#include<conio.h>
#define EST 0.05
#define F(x) exp(-x)-x
#define G(x) exp(-x)
int main()
{
int i=1;
float error,x0,x1,temp;
printf("Enter the initial guess x0:\n");
scanf("%f",&x0);
printf("Iteration x0\t\t x1\t Error\n");
x1=G(x0);
error=fabs((x1-x0)/x1);
printf("%d\t %.4f\t%.4f\t %.4f\n",i,x0,x1,error);
do
{
i++;
temp=x1;
x0=temp;
x1=G(x0);
error=fabs((x1-x0)/x1);
printf("%d\t %.4f\t%.4f\t %.4f\n",i,x0,x1,error); 
}while (error>EST);
}

C Program To Calculate Values Using Honors Method 

Pseudo Code

coefficients := [-19, 7, -4, 6] # list coefficients of all x^0..x^n in order

x := 3

accumulator := 0

for i in length(coefficients) down to 1 do

    # Assumes 1-based indexing for arrays

    accumulator := ( accumulator * x ) + coefficients[i]

done

# accumulator now has the answer

#include<stdio.h>

#include<conio.h>

#include<math.h>

//Given Polynomial = F(x) (4*x*x*x*x)+(5*x*x*x)+(6*x*x)+(7*x)+8

int main()

{

int i,x,n;

printf("Enter the degree of the polynomial:\n");

scanf("%d",&n);

int a[n+1],b[n+1];

printf("Enter the cofficient of polynomial starting from the higher degree:\n");

for(i=n;i>=0;i--)

{

scanf("%d",&a[i]);

}

printf("Enter the value at which polynomial has to be evaluated:\n");

scanf("%d",&x);

b[n]=a[n];

for(i=n-1;i>=0;i--)

{

b[i]=a[i]+(b[i+1]*x);

}

printf("The value of given polynomial at X=5 is %d.",b[0]);

}